Good points, all. “Head turned towards the viewer of the shield” is “g(u)ardant” (both spellings used, the “gardant” being preferred since the meaning is, roughly, “regarding” (looking at) the viewer). “Affrontee” means that the whole animal is facing front. So:
[ul][li]“rampant” means “rearing, body and head facing right as you see the shield”[/li][li] “rampant gardant” means “rearing, body facing right and head facing the viewer”[/li][li] “rampant affrontee” means “rearing, whole animal, both body and head, facing front”[/li][/ul]
The technical language is used out of tradition and combines two things: brevity (e.g., the inital “gules” means “the background color is spectrum red” in one word) and precision. E.g., “azure” is spectrum blue; there is also the rare “blue-celeste” for sky blue.
As far as ownership of arms goes, (1) they are personal – “your family coat of arms” is the product of a fast-buck artist playing on the misunderstanding of the general public that they are somehow “family” possessions – they are that only in that the right to them is inheritable.
(2) Title to them is awarded by appropriate officials in European countries (including Ireland and the U.K.) and applies to ownership under their laws.
(3) Since American citizens are collectively possessed of sovereignty, and forbidden (or at least discouraged; the law is subject to interpretation) to seek “titles of honor” from “foreign potentates,” a U.S. citizen should not matriculate foreign arms, but assume them if they are the heir of right. There is nothing preventing one from designing one’s own arms and using them; there are U.S. registries, without the force of law, for registering what one has chosen.
(4) The principle of comity between nations means that you should not assume a set of arms whose ownership belongs to somebody else overseas – just because your surname is Howard, for example, does not allow you to display the arms of the Duke of Norfolk. But many people take the arms of their family and differentiate them to make a “new” set for themselves. For example, should I ever want to display arms, I have the Wilbur arms with the tinctures reversed and a label of three to indicate being heir of line of a junior branch of the house.